Bruno, Thanks for the reference. That book sounds very interesting... unfortunately it is also very expensive.

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--Abram On Thu, Dec 25, 2008 at 1:23 PM, Bruno Marchal <marc...@ulb.ac.be> wrote: > > On 25 Dec 2008, at 08:05, Abram Demski wrote: > > Bruno, > > I agree with Gunther about the two types of machine. The broader > machine is any system that can be logically described-- a system that > is governed by rules and has a definite description. > > Then Church thesis entails it is not broader, unless you mean that the rules > are not effective. > > > Such machines are > of course not necessarily computable; oracle machines and so on can be > logically described (depending of course on the definition of the word > "logical", since they cannot be described using 1st-order logic with > its standard semantics). > > UDA still works with very big weakening of comp, which I don't mention > usually for pedagogical purpose. The fact that the first person cannot be > aware of delays, together with the fact that the UD generates the reals > extend the comp consequences to machine with all kind of oracles. > The AUDA is even less demanding, and works for highly non effective notion > of "belief". Instead of using the Gödel provability predicate we can use non > effective notion like "truth in all model of ZF", or even "truth in all > transitive models of ZF". In that last case G and G* can be effectively > extended. > To my knowledge the only scientist being explicitly non mechanist is > Penrose. Even Searle who pretends to be a non mechanist appears to refer to > machine, for the brain, which are Turing emulable. Then Searles make error > in its conception of "mind implementation" and "simulation" like Hofstadter > and Dennett have already very well criticized. The comp reasoning begins to > be in trouble with machines using discrete set of actual infinities. Analog > machine based on notion of interval are mostly Turing emulable. You have to > diagonalize or use other logical tools in some sophisticate way to build > analytical machine which are non turing emulable. Nothing in physics or in > nature points on the existence of those "mathematical weirdness", with the > notable "collapse of the wave packet" (exploited by Penrose, but also by > many dualists). > > > > > The narrower type of machine is restricted to be computable. > > It is logically narrower. But no weakening of comp based on nature is known > to escape the replicability. Even the non cloning theorem in QM cannot be > used to escape the UDA conclusion. You have to introduce explicit use of > actual infinities. This is very akin to a "substantialisation" of soul. I > respect that move, but I have to criticize unconvincing motivations for it. > Comp entails the existence of uncomputable observable phenomena. It is > normal to be attracted to the idea that non computability could play a role > in the mind. But this consists to build a machine based on the many sharable > computations going through the turing state of the machine and this gives > "quantum machine", which are turing emulable although not in real time, but > then they play their role in the Universal Deployment. > Of course you can just say "NO" to the doctor. But by invoking a non turing > emulable "machine", you take the risk of being asked which one. Up to now, > as far as I know, this exists in mathematics, but there are no evidence it > exists in nature, except those using the kind of indeterminacy which can be > explain with the comp hypothesis. > > > > All known physical causal system are Turing emulable. > > > I am no physicist, but I've been trying to look up stuff on that > issue... Schmidhuber asserts in multiple places that the fact that > differential equations are used to describe physics does not > contradict its computability, but he does not explain. > > The SWE is linear. It makes the quantum object directly turing emulable > (mostly by dovetailing if you are using a sequential processor). The > solution are linear combination of complex exponential. Obviously e, PI and > i are computable reals. > It is far more difficult, and perhaps false, to say that Newtonian Physics > is Turing emulable. Newton himself was aware of action at a distance for its > gravitational law. But anything so weird has been usually considered as an > evidence that Newtonian Physics could not be taken literaly. > To reintroduce such bizarre feature in nature just to contradict the comp > hyp is a bit ironical. It is like Bohmian reformulation of Quantum > Mechanics: to make a theory more complex to avoid interpretation judged as > unpleasant. > This subject is made difficult because there are no standard notion of > computability with the real numbers (despite many attempts to find one). > If someone know better ... Non comp theories have to be rather exotic. Of > course this is not an argument for the truth of comp. > > I know that, > for example, Wolfram is attempting a computable foundation for > physics, but I don't know about any real progress... so any info would > be appreciated. > > Wolfram like Schmidhuber believes there could be a computable universe. The > "whole" could be computable. But in that case the UDA shows that the > universe is a mathematical one, and indeed can be described by any universal > dovetailer. But the *physical* universe emerging from inside will have some > uncomputable feature. This comes from the fact that we are necessarily > ignorant about which computations support us, and that, below our > substitution level, we have to take into account of a a non enumerable set > of computations. (More in the UDA). > An interesting book on the computability with the reals containing some of > the construction mentioned above, is: > POUR-EL M. B., RICHARD J. I., 1989, Computability in Analysis and Physics, > Springer-Verlag, Berlin. > If I remember well you can find in this book a computable function having a > non computable derivative! > See also this link, and related links for the analog/digital problem, or > search on "universal analog machine" or "turing analog machine". > http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6V1G-4M6XMHG-3&_user=10&_rdoc=1&_fmt=&_orig=search&_sort=d&view=c&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=165aa939bc8414dbea9554ee03ea1b9e > > Bruno > http://iridia.ulb.ac.be/~marchal/ > > > > > > -- Abram Demski Public address: abram-dem...@googlegroups.com Public archive: http://groups.google.com/group/abram-demski Private address: abramdem...@gmail.com --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. 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